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55
a very conservative safety factor (FS = 3.66) relative to the database (Barker et al., 1991) and seem to be incompatible
static analysis methods. with any other source. The dataset for pipe piles in clay (Fig-
The major derived conclusions are therefore ure 46) seem to be sensitive to the elimination of the extreme
cases as shown by the relations between the resistance fac-
tors and target reliability for a set including 20, 19, 18, and
1. The absolute value of a safety measure (factor of safety
17 cases, associated with all data, data within the two stan-
or resistance factor) by itself does not represent the eco-
dard deviation zone, 1.5 SD zone, and 1SD zone respec-
nomics of the method or the progressiveness of the
tively. When examining the same design method for the data-
code as suggested in Table 1.
bases of concrete piles and H piles, the sensitivity of the
2. An efficiency factor or a similar parameter is required
exclusion of cases does not exist once the extreme cases
in order to account for the bias of the analysis methods
beyond the zone of two standard deviations are omitted.
and provide an objective evaluation regarding the effec-
Figures 49 through 52 relate to the analyses of driven piles
tiveness of the capacity prediction method.
in sand. The recommended factors seem to vary in relation to
3. Databases are essential to assess any design method-
the existing FS according to the pile type; matching the exist-
ology.
ing WSD for pipe piles, while being substantially higher for
4. The reduction of the factor of safety during design based
concrete piles and lower for H piles. This demonstrates the
on the anticipated capacity verification method during
effect of developing parameters with a consistent probability
construction is unreasonable and unsafe. Specifically, if
of failure compared to the parameters of the existing method-
one uses an FS = 2 for static analysis during design
ology. The new parameters may appear depending on the
because a static load test is expected to be carried out
case conservative or unsafe compared to existing standards,
during construction (see Table 1), the actual mean FS
while actually being consistent.
in these cases is about 1.5 (1.45 to 1.62 for and
The recommended resistance factors for redundant drilled
methods, respectively).
shafts, presented in Table 29, agree overall with those pro-
vided by the existing specifications. The categorization by
construction methods in mixed subsurface (sand and clay)
3.5.3 Sensitivity Analysis can be further evaluated in light of local practices. Specify-
and Factors Evaluation ing a construction method before bidding is permitted in
some states and not in others. Unspecific bidding specifica-
The existing resistance factors of the AASHTO specifica-
tions eliminate the possibility of a design associated with a
tions for dynamic evaluation of driven piles are limited and
specific construction method. The practice of constructing
connected to static evaluation methods. The recommended
single nonredundant drilled shafts is more common than in
resistance factors, presented in Table 27, are novel in their
the case of driven piles. For nonredundant drilled shafts, the
approach and categorization. Detailed comparisons between
recommended resistance factors are lower than the common
the current AASHTO specifications and those recommended
practice and need to be further evaluated in light of the pos-
are, therefore, not possible. General comparison between the
sible consequences of failure.
factors presented in Table 27 and those of other codes (e.g.,
Australia's) suggests that the proposed resistance factors are
comparable. 3.5.4 Actual Probability of Failure
The resistance factors for static analyses of driven piles, pre-
sented in Table 25, can be compared to the existing specifica- One advantage of using a large database is that the proba-
tions with the application of the v factor and neglecting the bility of failure (or the risk) can be directly calculated from
specific method of the recommended values. When compared, the available data, rather than by using the calculated distri-
the proposed parameters are reasonably in agreement with, but bution function. The procedure is done by applying a certain
demonstrate the weakness of, the existing specifications. resistance factor to the calculated resistance (capacity) and
A sensitivity analysis along with a comparison between examining the number of cases that exceed the actual capac-
the parameters of different sources for static analyses of ity (nominal strength). An example of the process as applied
driven piles is presented in Figures 45 through 52. Figure 45 to some of the dynamic methods is presented in Table 31. It
presents a summary of parameters from the existing LRFD should be noted that the values presented in Table 31 are con-
code, the Standard (WSD) AASHTO code and the present servative, as a comprehensive calculation should account for
recommended values. Figures 46 through 48 present a sensi- the load factors (on the order of 1.35 depending on the DL to
tivity analysis along with a comparison between the factors LL ratio); hence further decrease the probability of failure
for selected cases. For example Figure 46 examines the values provided in Table 31. The data in Table 31 suggests
dataset related to pipe piles in clay, analyzed using the API that the recommended factors presented in Table 27 would
method. The use of = 0.7 for the method in the existing result in target reliabilities higher (lower pf) than those cal-
LRFD AASHTO specifications is apparently based on a culated for using the distribution functions.
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0.80
y = 1.1267x
0.70
No. of points = 160
Mean = 1.148 FOSM = FORM
Std. Dev. = 0.039
0.60
Resistance factors using FORM
0.50
Driven Piles Static
0.40
Analysis
Driven Piles Dynamic
Analysis
0.30 Drilled Shafts Static
Analysis
FOSM = FORM
0.20
Linear Best-fit
0.10
0.00
- 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
Resistance factors
. using FOSM
Figure 41. Comparison between resistance factors obtained using the First Order
Second Moment (FOSM) vs. those obtained by using First Order Reliability Method
(FORM) for a target reliability of = 2.33.
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TABLE 19 Statistical details of static analyses of driven piles, resistance factors, efficiency factors, equivalent
and "actual" factors of safety
N No. of =2.33 =3.00
=3
Soil Pile Details of Method(2) Mean
Total No. Design Method(1) Cases COV
Type Type Application () / FS FS x / FS x
of Cases ± 2 SD FS
4 -Method 11.5 B;T&P(2) 4 0.61 0.61 0.19 0.32 7.34 4.48 0.13 0.22 10.63 6.48
17 -Method 11.5B; T&P(2) 2B; T&P(5) 16 0.74 0.39 0.37 0.50 3.80 2.82 0.29 0.39 4.97 3.68
H-Piles 17 -Tomlinson 2B; T&P(2) 17 0.82 0.40 0.40 0.49 3.51 2.88 0.31 0.37 4.61 3.78
17 -API 2B; T&P(5) 16 0.90 0.41 0.43 0.48 3.26 2.93 0.33 0.37 4.30 3.87
9 SPT-97 mob 8 1.04 0.41 0.50 0.48 2.84 2.95 0.38 0.36 3.74 3.89
19 -Method 2B; Hara (5h) 18 0.76 0.29 0.48 0.63 2.97 2.26 0.38 0.51 3.69 2.80
Concrete 19 -API 2B; Hara (5h) 17 0.81 0.26 0.54 0.67 2.61 2.11 0.44 0.55 3.20 2.59
Clay
Piles 8 -Method 2B; Hara (5h) 8 0.81 0.51 0.32 0.39 4.45 3.60 0.23 0.28 6.14 4.97
19 -Tomlinson 2B; Hara (5h) 18 0.87 0.48 0.36 0.41 3.94 3.43 0.26 0.30 5.37 4.67
20 -Tomlinson 2B; T&P (1) 18 0.64 0.50 0.25 0.40 5.56 3.56 0.19 0.29 7.64 4.89
20 -API 2B; T&P (1) 19 0.79 0.54 0.29 0.36 4.95 3.91 0.20 0.26 6.96 5.50
Pipe
13 -Method 2B; T&P (1) 12 0.45 0.60 0.14 0.32 9.81 4.41 0.10 0.22 14.16 6.37
Piles
20 -Method 2B; T&P (1) 19 0.67 0.55 0.24 0.36 5.94 3.98 0.17 0.25 8.38 5.62
13 SPT-97 mob 2B; T&P (1) 12 0.39 0.62 0.12 0.31 11.70 4.56 0.08 0.21 17.02 6.64
19 Nordlund 36; 11.5B,P(6) 19 0.94 0.40 0.46 0.49 3.08 2.89 0.35 0.37 4.04 3.80
19 Meyerhof 18 0.81 0.38 0.42 0.51 3.41 2.76 0.32 0.39 4.43 3.59
H-Piles
19 -Method 36; 2B; P(5) 19 0.78 0.51 0.30 0.39 4.69 3.66 0.22 0.28 6.49 5.06
19 SPT-97 mob 18 1.35 0.43 0.63 0.46 2.26 3.05 0.47 0.35 3.01 4.06
37 Nordlund 36: 11.5B; P(6) 36 1.02 0.48 0.42 0.42 3.34 3.41 0.31 0.31 4.55 4.64
Concrete 37 -Method 36; 2B; P(5) 35 1.10 0.44 0.50 0.46 2.82 3.10 0.38 0.34 3.76 4.13
Sand
Piles 37 Meyerhof 36 0.61 0.61 0.19 0.32 7.34 4.48 0.13 0.22 10.63 6.48
37 SPT97 mob 36 1.21 0.47 0.51 0.42 2.76 3.34 0.38 0.31 3.75 4.53
20 Nordlund 36; 2B P(5) 19 1.48 0.52 0.56 0.38 2.51 3.71 0.41 0.27 3.49 5.16
Pipe 20 -Method 36; 2B P(5) 20 1.18 0.62 0.36 0.31 3.89 4.59 0.25 0.21 5.67 6.69
Piles 20 Meyerhof 20 0.94 0.59 0.31 0.33 4.55 4.27 0.22 0.23 6.52 6.13
20 SPT-97 mob 19 1.58 0.52 0.60 0.38 2.34 3.70 0.44 0.28 3.26 5.14
22 -Tomlinson/Nordlund/Thurman 36; 2B; P(5) 20 0.59 0.39 0.30 0.51 4.75 2.80 0.23 0.39 6.20 3.66
37 -API/Nordlund/Thurman 36; 2B; P(5) 34 0.79 0.44 0.36 0.45 3.98 3.14 0.27 0.34 5.33 4.21
H-Piles
35 -Method/Thurman 36; 2B; P(5) 32 0.48 0.48 0.20 0.42 7.08 3.40 0.15 0.31 9.65 4.63
41 SPT-97 40 1.23 0.45 0.55 0.45 2.58 3.17 0.41 0.33 3.46 4.25
34 -Tomlinson/Nordlund/Thurman 36; 2B; P; Hara(5h) 33 0.96 0.49 0.39 0.41 3.62 3.48 0.29 0.30 4.96 4.76
85 -API/Nordland/Thurman 36; 11.5B; Sch; T&P(8) 80 0.87 0.48 0.36 0.41 3.94 3.43 0.26 0.30 5.37 4.67
Mixed Concrete
85 -Method/Thurman 36; 11.5B; Sch; T&P(8) 80 0.81 0.38 0.42 0.51 3.41 2.76 0.32 0.39 4.43 3.59
Soils Piles
74 SPT-97 mob 71 1.81 0.50 0.72 0.40 1.98 3.58 0.52 0.29 2.72 4.93
32 FHWA CPT 30 0.84 0.31 0.51 0.60 2.81 2.36 0.40 0.48 3.52 2.96
13 -Tomlinson/Nordlund/Thurman 36; 2B; P(5) 13 0.74 0.59 0.24 0.32 5.89 4.36 0.17 0.23 8.49 6.28
Pipe 34 -API/Nordland/Thurman 36; 2B; P(5) 32 0.80 0.45 0.36 0.44 3.99 3.19 0.26 0.33 5.36 4.29
Piles 31 -Method/Thurman 36; 2B; P(5) 29 0.54 0.48 0.22 0.41 6.33 3.42 0.16 0.30 8.63 4.66
34 SPT-97 mob 33 0.76 0.38 0.39 0.51 3.62 2.75 0.30 0.40 4.71 3.58
(1)
See Table 6 for details;
(2)
Numbers in parentheses refer to notations used for detailing soil parameter combinations (see Table 7b and Appendix C for more details), See Tables 7a and 8 for soil
properties' correlations to SPT and CPT respectively, 36 = limiting friction angle, B = pile diameter 2B, 11.5B contributing zone to tip resistance.
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TABLE 20 Statistical details of dynamic analyses of driven piles, resistance factors, efficiency factors, equivalent
and "actual" factors of safety
No. of Mean = 2.33 = 3.0
Method Time of Driving COV
Cases () / F.S. F.S.x / F.S F.S.x
General 377 1.368 0.453 0.59 0.43 2.40 3.28 0.43 0.31 3.29 4.51
EOD 125 1.626 0.490 0.64 0.40 2.21 3.60 0.46 0.28 3.08 5.01
Dynamic Measurements
CAPWAP EOD - AR < 350 &
37 2.589 0.921 0.41 0.16 3.46 8.95 0.23 0.09 6.16 15.95
Bl. Ct. < 16 BP10cm
BOR 162 1.158 0.339 0.65 0.56 2.18 2.52 0.51 0.44 2.78 3.22
General 371 0.894 0.411 0.42 0.47 2.52 2.26 0.32 0.36 4.43 3.96
EOD 128 1.084 0.398 0.53 0.49 2.67 2.91 0.40 0.37 3.54 3.84
Energy
Approach EOD - AR < 350 &
39 1.431 0.508 0.54 0.38 2.62 3.75 0.39 0.27 3.63 5.20
Bl. Ct. < 16 BP10cm
BOR 153 0.785 0.369 0.41 0.52 3.46 2.71 0.32 0.41 4.43 3.48
ENR General 384 1.602 0.910 0.26 0.16 5.45 8.73 0.15 0.09 9.45 15.13
Gates General 384 1.787 0.475 0.73 0.41 1.94 3.47 0.53 0.30 2.67 4.78
Equations
Dynamic
General 384 0.940 0.502 0.36 0.38 3.94 3.70 0.26 0.38 5.45 5.12
FHWA
modified EOD 135 1.073 0.534 0.38 0.36 3.73 4.00 0.27 0.25 5.25 5.63
Gates EOD
62 1.306 0.492 0.51 0.39 2.78 3.63 0.37 0.28 3.83 5.00
Bl. Ct. < 16BP10cm
WEAP EOD 99 1.656 0.724 0.39 0.24 3.63 6.02 0.25 0.24 5.67 9.38
Notes: Column heads: Mean = ratio of the static load test results (Davisson's Criterion) to the predicted capacity = Ksx = = bias;
COV = Coefficient of Variation
Methods: ENR = Engineering News Record Equation
Time of Driving: EOD = end of driving; BOR = beginning of restrike; AR = area ratio; Bl. Ct. = blow count;
BP10cm = blows per 10cm
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TABLE 21 Statistical details of static analyses of drilled shafts, resistance factors, efficiency factors, equivalent
and "actual" factors of safety
Capacity Soil
N
Design Const.
No. of Mean = 2.33 = 3.0
Total No. Cases COV
Component Type Method Method () / F.S. F.S. x / F.S. F.S. x
of Cases ± 2 SD
34 Mixed 32 1.71 0.60 0.55 0.32 2.58 4.41 0.38 0.22 3.73 6.37
14 FHWA Casing 12 2.27 0.46 0.99 0.43 1.44 3.26 0.73 0.32 1.94 4.40
14 Slurry 9 1.62 0.74 0.38 0.24 3.69 5.97 0.25 0.15 5.70 9.23
Sand
34 Mixed 32 1.22 0.67 0.34 0.28 4.21 5.13 0.23 0.18 6.29 7.67
14 R&W Casing 12 1.45 0.50 0.58 0.40 2.45 3.56 0.42 0.29 3.37 4.89
14 Slurry 9 1.32 0.62 0.41 0.31 3.49 4.61 0.28 0.21 5.09 6.72
54 Mixed 53 0.90 0.47 0.38 0.43 3.70 3.33 0.28 0.31 5.02 4.52
Clay 14 FHWA Casing 13 0.84 0.50 0.33 0.40 4.23 3.56 0.24 0.29 5.82 4.89
40 Dry 40 0.88 0.48 0.37 0.42 3.87 3.41 0.27 0.31 5.27 4.64
Skin Friction 48 Mixed 44 1.19 0.30 0.73 0.61 1.94 2.31 0.58 0.49 2.42 2.88
+ 23 Casing 21 1.04 0.29 0.65 0.63 2.17 2.26 0.52 0.50 2.70 2.81
End Bearing FHWA
13 Dry 12 1.32 0.28 0.85 0.64 1.67 2.21 0.68 0.52 2.07 2.73
Sand + 12 Slurry 10 1.29 0.27 0.84 0.65 1.68 2.16 0.69 0.53 2.06 2.66
Clay 48 Mixed 44 1.09 0.35 0.60 0.55 2.36 2.57 0.47 0.43 3.02 3.29
23 Casing 21 1.01 0.42 0.48 0.47 2.96 2.99 0.36 0.36 3.92 3.96
R&W
13 Dry 12 1.20 0.32 0.71 0.59 2.01 2.41 0.56 0.47 2.53 3.04
12 Slurry 10 1.16 0.25 0.79 0.68 1.79 2.07 0.65 0.56 2.18 2.53
49 Mixed 46 1.23 0.41 0.60 0.48 2.38 2.93 0.45 0.37 3.13 3.86
C&K
32 Dry 29 1.29 0.40 0.64 0.49 2.22 2.86 0.49 0.38 2.91 3.76
Rock
49 Mixed 46 1.30 0.34 0.73 0.56 1.94 2.52 0.57 0.44 2.46 3.20
IGM
32 Dry 29 1.35 0.31 0.81 0.60 1.75 2.36 0.65 0.48 2.19 2.96
11 FHWA Mixed 11 1.09 0.51 0.43 0.39 3.33 3.63 0.31 0.28 4.61 5.02
Sand
11 R&W Mixed 11 0.83 0.54 0.30 0.37 4.67 3.88 0.22 0.26 6.55 5.44
Clay 16 FHWA Mixed 13 0.87 0.37 0.46 0.53 3.09 2.69 0.36 0.41 3.99 3.47
Sand + 16 FHWA Mixed 14 1.25 0.29 0.78 0.63 1.81 2.26 0.63 0.50 2.25 2.81
Skin Clay 16 R&W Mixed 14 1.24 0.41 0.60 0.48 2.36 2.93 0.46 0.37 3.11 3.86
All 40 FHWA Mixed 39 1.08 0.41 0.52 0.48 2.71 2.93 0.40 0.37 3.57 3.86
Soils 27 R&W Mixed 25 1.07 0.48 0.45 0.42 3.18 3.41 0.33 0.31 4.34 4.64
17 C&K Mixed 16 1.18 0.46 0.51 0.43 2.76 3.26 0.38 0.32 3.73 4.40
Rock
17 IGM Mixed 16 1.25 0.37 0.66 0.53 2.15 2.69 0.51 0.41 2.78 3.47
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TABLE 22 Resistance factors and associated factors of safety along with efficiency measures
for sample methods
= 2.33
L = 1.75, D = 1.2, DL/LL = 2
Pile Type or Soil Type or Method of = 3.00
Category FS FS x
Construction State Analysis /
resistance factor of actual
efficiency
factor safety mean FS
0.54 0.67 2.61 2.11
PPC Cl ay - API
0.44 0.55 3.20 2.59
Static Methods 0.50 0.46 2.82 3.10
Driven Piles PPC Sand
0.38 0.34 3.76 4.13
- API 0.36 0.44 3.99 3.19
Pipe Mixed
Nordlund/Thurman 0.26 0.33 5.36 4.29
0.65 0.56 2.18 2.52
All BOR CAPWAP
Dynamic 0.51 0.44 2.78 3.22
Methods 0.53 0.49 2.67 2.91
All EOD Energy Approach
Driven Piles 0.40 0.37 3.54 3.84
0.38 0.36 3.73 4.00
All EOD FHWA mod Gates
0.27 0.25 5.25 5.63
0.45 0.42 3.18 3.41
Mixed All R&W skin
0.33 0.31 4.34 4.64
Static Methods 0.60 0.48 2.38 2.93
Drilled Shafts Mixed Rock C&K total
0.45 0.37 3.13 3.86
0.78 0.63 1.81 2.26
Mixed Sand & Clay FHWA skin
0.63 0.50 2.25 2.81
Notes: *Top line of column: = 2.33; **Bottom line of column: = 3.00; L = 1.75; D = 1.2; DL/LL = 2.
TABLE 23 Detailed resistance factors for pullout of driven piles--based on static analyses
Resistance Factor /
Pile Soil Design No. Non- Non-
COV Redundant Redundant
Type Type Method redundant redundant
= 2.33 = 2.33
= 3.00 = 3.00
-API 9 1.11 0.71 0.28 0.18 0.25 0.16
Clay -Tomlinson 9 0.95 0.57 0.33 0.23 0.35 0.24
Pipe -Method 9 0.72 0.52 0.27 0.20 0.38 0.36
Sand -Method 7 0.52 0.54 0.19 0.14 0.37 0.27
and SPT-97 mob 7 1.18 1.33 0.08 0.04 0.07 0.03
Mixed API/Nordlund 7 0.80 0.60 0.26 0.18 0.33 0.23
-API 3 0.76 0.57 0.26 0.18 0.34 0.24
Clay
-Tomlinson 3 0.64 0.54 0.23 0.17 0.36 0.27
H
Sand -Method 8 0.23 0.36 0.12 0.10 0.52 0.43
SPT-97 mob 8 0.43 0.32 0.25 0.20 0.58 0.47
TABLE 24 Resistance factors as a function of number of load tests per site, site variability
and target reliability
Site Variation N Mean SD C.O.V. Target Reliability
() (Bias) 2.00 2.33 3.00
1 1 0.18 0.18 0.86 0.80 0.67
2 1 0.13 0.13 0.96 0.89 0.78
Low 3 1 0.10 0.10 1.00 0.94 0.83
4 1 0.09 0.09 1.03 0.97 0.86
5 1 0.08 0.08 1.04 0.99 0.88
1 1 0.27 0.27 0.73 0.65 0.53
2 1 0.19 0.19 0.85 0.78 0.66
Medium 3 1 0.16 0.16 0.90 0.84 0.72
4 1 0.14 0.14 0.94 0.88 0.76
5 1 0.12 0.12 0.97 0.90 0.79
1 1 0.36 0.36 0.61 0.54 0.42
2 1 0.25 0.25 0.75 0.68 0.55
High 3 1 0.21 0.21 0.82 0.75 0.63
4 1 0.18 0.18 0.86 0.80 0.67
5 1 0.16 0.16 0.90 0.83 0.71
Note: N = Number of load tests
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Acceptance criterion x*
Distribution of unac-
ceptable set of piles
Frequency
Buyer's risk
Distribution of ac-
ceptable set of piles
Seller's risk
Frequency
Pile Capacity
Figure 42. Frequency distributions of test results
taken from sets of unacceptable and acceptable piles,
showing contractor's (seller's) and owner's (buyer's)
risks (schematic).
1.00
Owner's risk: 1-=0.90
0.80
Probability of Acceptance
0.60
0.40
0.20
Contractor's risk: =0.10
0.00
400 500 600 700 800 900 1,000
Mean Pile Capacity (kips)
Figure 43. Operating characteristics curve for an acceptance sampling plan
to ensure the average axial capacity of a set of piles.
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62
0.01
0.1
0.05
110 0.90
2
Figure 44. Binomial nomograph for determining sample size, n, and permitted number of defectives, c,
for contractor's risk and owner's risk (Montgomery 1991). The procedure for using the nomograph to
design a sampling plan is to (1) draw a line connecting on the right-hand rule with the corresponding p1
on the left-hand rule, (2) draw a similar line connecting (1-) and p2, and (3) the point of intersection of
the two lines gives the required sample size, n, and the maximum number of defectives permitted within the
sample for acceptance.
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TABLE 25 Recommended resistance and efficiency factors for static analyses of driven piles
Resistance Factor /
Soil Design Non- Non-
Pile Type
Type Method Redundant redundant Redundant redundant
Mixed SPT-97 mob 0.70 0.50 0.40 0.29
Clay -API 0.67 0.55
-Method 0.63 0.55
-Method 0.50 0.40 0.46 0.34
Sand
SPT-97 mob 0.42 0.31
Concrete FHWA CPT 0.60 0.48
Pile Mixed -Method/Thurman 0.51 0.39
Tomlinson/Nordlund/Thurman 0.40 0.30 0.41 0.30
Sand Nordlund 0.42 0.31
Clay -Tomlinson 0.41 0.30
0.35 0.25
Mixed -API/Nordlund/Thurman 0.41 0.30
Sand Meyerhof 0.20 0.15 0.32 0.22
Sand SPT-97 mob 0.55 0.45 0.38 0.28
Nordlund 0.38 0.27
SPT-97 mob 0.40 0.30 0.51 0.40
Mixed
-API/Nordlund/Thurman 0.44 0.31
0.35 0.25
Sand -Method 0.31 0.21
.
Pipe Pile Clay -API 0.36 0.26
0.30 0.20
Sand Meyerhof 0.33 0.23
Tomlinson/Nordlund/Thurman 0.32 0.23
Mixed
-Method/Thurman 0.41 0.30
0.25 0.15
-Tomlinson 0.40 0.29
Clay
-Method 0.36 0.25
Mixed SPT-97 mob 0.45 0.33
0.55 0.45
SPT-97 mob 0.46 0.35
Sand Nordlund 0.49 0.37
Meyerhof 0.45 0.35 0.51 0.39
-API 0.48 0.37
H Piles
Clay -Tomlinson 0.49 0.37
0.40 0.30
-Method 0.50 0.39
-API/Nordlund/Thurman 0.35 0.45 0.34
Mixed
Tomlinson/Nordlund/Thurman 0.25 0.51 0.39
0.30
Sand -Method 0.39 0.28
Mixed -Method/Thurman 0.20 0.15 0.42 0.31
Notes: / = efficiency factor, evaluating the relative economic performance of each method (higher ratios indicate a more
economical solution).
= bias = Ksx = Mean of measured over predicted.
/ values relate to the exact calculated and and not to the assigned values in the table
Redundant = Five piles or more under one pile cap ( = 2.33 pf = 1.0%)
Non-Redundant = Four or fewer piles under one pile cap ( = 3.0 pf = 0.1%)
TABLE 26 Recommended resistance factors for static analysis
of nontapered driven piles under pullout
(resistance factor)
Soil Type Design Method Pile Type Redundant Non-Redundant
= 2.33 = 3.00
-API,
Clay H, Pipe, PPC 0.251 0.20
Tomlinson
H 0.15 0.10
Sand Pipe, PPC 0.25 0.20
SPT-97 H, Pipe, PPC 0.25 0.20
Mixed -API/Nordlund H, Pipe, PPC 0.20 0.15
1
Higher values may be applicable for PPC piles but no sufficient data were available to support this.
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TABLE 27 Recommended resistance and efficiency factors for dynamic analyses of driven piles
(resistance factor) /
Method Case
Redundant Non-Redundant Redundant Non-Redundant
EOD 0.65 0.45 0.40 0.28
Signal
Matching EOD, AR<350,
0.40 0.25 0.16 0.09
Dynamic (CAPWAP)
Bl. Ct.<16BP10cm
Measurements BOR 0.65 0.50 0.56 0.44
Energy EOD 0.55 0.40 0.49 0.37
Approach BOR 0.40 0.30 0.52 0.41
ENR General 0.25 0.15 0.16 0.09
Dynamic Gates General 0.75 0.55 0.41 0.30
Equations FHWA
General 0.40 0.25 0.38 0.28
modified
WEAP EOD 0.40 0.25 0.24 0.15
Notes: COV = Coefficient of Variation
Column heads: / = efficiency factor, evaluating the relative economic performance of each method (higher
ratios indicate a more economical solution); / values relate to the exact calculated and and
not to the assigned values in the table; Redundant = Five piles or more under one pile cap.( = 2.33
pf = 1.0%); = bias = KSX = Mean of measured/predicted; Non-Redundant = Four or less piles
under one pile cap ( = 3.0 pf = 0.1%)
Method: ENR = Engineering News Record Equation.
Case: EOD = End of Driving; BOR = Beginning of Restrike; AR = Area ratio; Bl.Ct. = blow count;
BP10cm = blows per 10cm
TABLE 28 Recommended number of dynamic tests
to be conducted during production
Site Variability. Low Medium High
No. of Method EA CAPWAP EA CAPWAP EA CAPWAP
Piles Time EOD BOR EOD BOR EOD BOR
15 4 3 5 4 6 6
16 - 25 5 3 6 5 9 8
26 - 50 6 4 8 6 10 9
51 100 7 4 9 7 12 10
101 500 7 4 11 7 14 12
> 500 7 4 12 7 15 12
Notes: Site variability see section 3.4.3, item 4 for the determination of site variability.
EA = Energy Approach Analysis; CAPWAP = Signal Matching Analysis;
EOD = End of Driving; BOR = Beginning of Restrike
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TABLE 29 Recommended resistance factors for drilled shafts
Shaft Soil Design Construction (resistance Factors) /
Resistance Type Method Method Non- Non-
Redundant Redundant
Redundant Redundant
0.36 0.29
R&W
Sand All 0.50 0.40
0.38 0.31
FHWA
Clay FHWA All 0.40 0.30 0.43 0.31
Slurry &
0.85 0.70 0.63 0.52
Dry
Total FHWA
Resistance Casing 0.65 0.50 0.63 0.52
Sand +
Clay Slurry &
0.75 0.60 0.65 0.52
Dry
R&W
Casing 0.50 0.35 0.47 0.36
Rock C&K All 0.60 0.60 0.48 0.37
IGM All 0.75 0.75 0.56 0.44
All FHWA All 0.45 0.35 0.48 0.40
Skin Soils R&W 0.42 0.33
Resistance C&K 0.50 0.35 0.43 0.32
Rock All
IGM 0.65 0.50 0.53 0.41
Notes: / = efficiency factor, evaluating the relative economic performance of each method (higher ratios
indicate a more economical solution); / values relate to the exact calculated and and
not to the assigned values in the table.
Redundant = Five piles or more under one pile cap ( = 2.33 pf = 1.0%)
Non-Redundant = Four or fewer piles under one pile cap ( = 3.0 pf = 0.1%)
= bias = KSX = mean of measured/predicted
FHWA = Reese and O'Neill (1988); R&W = Reese and Wright (1977);
C&K = Carter and Kulhawy (1988); IGM = O'Neill and Reese (1999).
TABLE 30 Recommended resistance factors
for static load tests
(Resistance Factor)
No. of Site Variability
Load Tests
Per Site Low Medium High
1 0.80 0.70 0.55
2 0.90 0.75 0.65
3 0.90 0.85 0.75
4 0.90 0.90 0.80
Note: Site variability: see section 3.4.3 item 4 for the determination of site
variability.
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Recommended values for = 2.33 Existing LRFD values
Pile Method Method 0.70 v
Type Method 0.55 v
Concrete 0.50 0.35 0.50 Method and Nordlund applied 0.50 v
for clay
Pipe 0.30 0.25 0.25
H 0.45 0.40 0.40
End Bearing Skempton 0.70 v
1. Suggest to omit Method in clay. Not considered WSD FS = 3.5
Nordlund in clay
2. FHWA CPT mixed soil concrete piles = 0.50
No./Mean of Prediction (data ± 2 SD)
Pile Type Method
API Tomlinson
Concrete 17 0.81 18 0.87 18 0.76
Pipe 19 0.79 18 0.64 19 0.67
H 16 0.90 17 0.82 16 0.74
Total 52 0.83 51 0.81 53 0.72
Actual Mean FS for driven piles in clay
Method = 0.82 x 3.5 = 2.87
Method = 0.72 x 3.5 = 2.52
For Comparison
CAPWAP - EOD 126 cases Mean = 1.63
BOR 162 Mean = 1.16
Actual FS EOD = 1.63 x 2.25 = 3.66
Actual FS BOR = 1.16 x 2.25 = 2.61
Figure 45. Data summary for parameter evaluation of driven piles in clay.
1
Pipe Piles - API
0.9 1 SD (17)
1.5 SD (18)
2 SD (19)
0.8
all data (20)
recommended
Method Exist
0.7
- Resistance Factor
0.6
Method Exist
Actual Mean FS = 2.77
0.5
0.4 FS = 3.5 WSD
0.3
0.2
0.1
0
1.5 2 2.5 3 3.5
- Target Reliability
Figure 46. Sensitivity analysis examining the recommended
parameters for the design of pipe piles in clay using API method.
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1
0.9
0.8
Method Exist
0.7
- Resistance Factor
0.6
Method Exist
Actual Mean FS = 2.84
0.5
FS = 3.5 WSD
0.4
0.3
Concrete Piles - API
0.2
0.1
0
1.5 2 2.5 3 3.5
- Target Reliability
Figure 47. Sensitivity analysis examining the recommended
parameters for the design of concrete piles in clay using API
method.
1
0.9
0.8
Method Exist
0.7
- Resistance Factor
0.6
Method Exist
0.5
Actual Mean FS = 3.15
0.4 FS = 3.5 WSD
0.3
H Piles - API
0.2 1 SD (12)
1.5 SD (15)
2 SD (16)
0.1 all data (17)
recommended
0
1.5 2 2.5 3 3.5
- Target Reliability
Figure 48. Sensitivity analysis examining the recommended
parameters for the design of H piles in clay using API method.
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Existing LRFD values skin
Recommended values for = 2.33 and end bearing
Pile Method CPT 0.55 v
Type
Nordlund Meyerhof SPT 97 SPT 0.45 v
Concrete 0.40 0.20 0.5 0.50 WSD FS = 3.5
Pipe 0.55 0.30 0.3 0.55
Actual mean FS for driven piles
H 0.45 0.45 0.3 0.55
in sand
FHWA CPT mixed soil concrete piles = 0.50
Range:
pipe piles SPT 97 = 1.58 x 3.5 = 5.53
No./Mean of prediction (data ± 2 SD) Meyerhof PPC = 0.61 x 3.5 = 2.14
Pile Method
Type Nordlund Meyerhof SPT 97
Concrete 36 1.02 36 0.61 35 1.10 36 1.21
Pipe 19 1.48 20 0.94 20 1.18 19 1.58
H 19 0.94 18 0.81 19 0.78 18 1.35
Total 74 1.18* 74 0.75* 74 1.04* 73 1.34*
* - large variation between pile types
Figure 49. Data summary for parameter evaluation of driven piles in sand.
1
0.9
Pipe Piles - Method
1 SD (13)
0.8
1.5 SD (18)
2 SD (20)
0.7 all data (20)
- Resistance Factor
recommended
0.6
0.5
0.4 FS = 3.5 WSD
Actual Mean FS = 4.13
0.3
0.2
0.1
0
1.5 2 2.5 3 3.5
- Target Reliability
Figure 50. Sensitivity analysis examining the recommended
parameters for the design of pipe piles in sand using the method.
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1
Concrete Piles - Method
0.9 1 SD (28)
1.5 SD (31)
2 SD (35)
0.8
all data (37)
recommended
0.7
- Resistance Factor
0.6
0.5
FS = 3.5 WSD
0.4
Actual Mean FS = 3.85
0.3
0.2
0.1
0
1.5 2 2.5 3 3.5
- Target Reliability
Figure 51. Sensitivity analysis examining the recommended
parameters for the design of concrete piles in sand using the
method.
1
H Piles - Method
0.9 1 SD (13)
1.5 SD (16)
2 SD (19)
0.8
all data (19)
recommended
0.7
- Resistance Factor
0.6
Actual Mean FS = 2.73
0.5
0.4 FS = 3.5 WSD
0.3
0.2
0.1
0
1.5 2 2.5 3 3.5
- Target Reliability
Figure 52. Sensitivity analysis examining the recommended
parameters for the design of H piles in sand using the method.
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TABLE 31 Calculated probability of failure [ p = (%)] based on direct utilization
of database PD/LT 2000 for selected prediction methods
Resistance CAPWAP Energy FHWA
factor CAPWAP CAPWAP EOD Approach Mod
General BOR AR > 350 EOD Gates
BL ct. > 16 BP10cm General
0.5 0.27 0 2.70 1.56 10.42
0.4 0 0 0 0 3.13
0.33 0 0 0 0 0.78
# of cases used 377 162 37 128 384
